Self-Checking Flow Meter and Method

ABSTRACT

A self-checking ultrasonic flow meter for measuring fluid flow in a conduit which includes a plurality of transducers engaged with the conduit. The flow meter includes a signal processor in electrical communication with the transducers which produces a measurement of flow rate and an associated estimate of uncertainty due to changes that have affected the accuracy of the measured flow rate. The transducers form multiple transducer pairs positioned to form acoustic transmission paths that are co-located in two or more chordal measurement planes. A method for measuring fluid flow in a conduit with an ultrasonic flow meter.

FIELD OF THE INVENTION

The present invention is related to a self-checking flow meter based onthe principles of ultrasonic transit time measurement. The flow metertherefore outputs a measurement of flow rate and an associated estimateof uncertainty due to changes that may have affected the accuracy of themeasurement system. In particular, the invention enables verification ofthe axial velocity in each chordal measurement plane of the flow meter.This technique enables accurate self-verification to be carried out inthe presence of complex non-axial flows including asymmetric rotationalflows, and in case of a discrepancy allows identification of the chordalmeasurement plane or planes that have contributed to the discrepancy. Italso uniquely allows identification of common-mode errors due tocontamination based on the measurements in individual chordalmeasurement planes. (As used herein, references to the “presentinvention” or “invention” relate to exemplary embodiments and notnecessarily to every embodiment encompassed by the appended claims.)

BACKGROUND OF THE INVENTION

This section is intended to introduce the reader to various aspects ofthe art that may be related to various aspects of the present invention.The following discussion is intended to provide information tofacilitate a better understanding of the present invention. Accordingly,it should be understood that statements in the following discussion areto be read in this light, and not as admissions of prior art.

Transit time ultrasonic flow meters are capable of high accuracyperformance over a wide range of application conditions. This has led totheir adoption in applications such as custody transfer of hydrocarbons,and measurement of nuclear feedwater flows.

To achieve high accuracy it is common for transit time ultrasonic flowmeters to employ multiple pairs of transducers to infer velocity on anumber of discrete paths. The velocity measurements can then becombined, along with information on geometry, to produce a measure ofvolumetric flowrate.

Two features of ultrasonic meters are particularly attractive in manyapplications. Firstly, they can be designed to be non-intrusive, that isto present no blockage to the flow, and consequently produceinsignificant pressure loss. Secondly, their self-diagnosticcapabilities are attractive in applications where routine in-situcalibration is difficult for practical or cost reasons.

Currently the self-diagnostic capabilities of transit time ultrasonicmeters are based on evaluation of parameters such as amplifier gain,signal-to-noise ratios, and velocity profile descriptors such asflatness, asymmetry and swirl [Peterson, S, Lightbody, C, Trail, J andCoughlan, L (2008) On-line condition based monitoring of gas USM's,Proceedings of the North Sea Flow Measurement Workshop, Scotland,October 2008; Kneisley, G, Lansing, J, Dietz, T (2009) Ultrasonic metercondition based monitoring—a fully automated solution, Proceedings ofthe North Sea Flow Measurement Workshop, Norway, October 2009.].However, as these parameters are difficult to relate directly to theuncertainty of the flow measurement, the use of meter diagnostics aloneis not presently regarded as sufficient as a means of flow meterverification. For example, in the UK the Measurement Guidelines of theoffshore oil and gas measurement regulator, while recognizing thebenefits of current diagnostic techniques, note that they have thedisadvantage that “diagnostic facilities are presently qualitative,rather than quantitative” [Department of Trade and Industry, Licensingand Consents Unit, Guidance Notes for Petroleum Measurement Under thePetroleum (Production) Regulations, December 2003, Issue 7.]. In orderto overcome this limitation, sometimes two flow meters are installed inseries, i.e. with one a short distance downstream of the other. Thisallows the volumetric flowrates from the two flow meters to be comparedwith one another, with the result that the verification is quantitative,rather than qualitative. Taking this concept a step further, it has alsobeen known to calculate two independent flow rate measurements using twoindependent subsets of transducers installed in a single meter body.

One example of such a meter design is the combination of a 4-path meterand a single path meter [Kneisley, G, Lansing, J, Dietz, T (2009)Ultrasonic meter condition based monitoring—a fully automated solution,Proceedings of the North Sea Flow Measurement Workshop, Norway, October2009], as illustrated in FIG. 1. A disadvantage of this design is thatthe single path meter is much more sensitive to distortions of the flowvelocity field than the 4-path meter. This difference in sensitivitymeans that when a difference is detected, there exists the possibilitythat the single path meter can be affected by a distortion of the flowfield that has a negligible effect on the 4-path meter. In the casewhere the four path meter is used as the primary measurement, this couldresult in false alarms, i.e. the difference detected does not reflect areduction in accuracy of the 4-path meter. For example, in thereferenced paper it is shown that when a flow conditioner upstream ofthe meter has one hole become blocked, there is virtually no effect onthe 4-path meter, whereas the effect on the single-path meter can begreater than 0.85%. If, for example, an alarm threshold of 0.5% was setfor the difference between the 4-path and single path result, theoutcome would be an alarm annunciation where in fact the 4-path meter iscontinuing to read accurately.

Other examples of this concept include using two similar but separategroups of ultrasonic paths, such as shown in FIGS. 2 a, 2 b, 3 a and 3b. FIGS. 2 a and 2 b show an arrangement of eight paths where one set offour paths are all set at a first angle relative to the pipe axis andthe second set of four paths are all set at the negative value of thatangle, such that the paths form a symmetrical X about the pipe axis whenviewed from above. In this example the first set of four paths would be1, 2, 3 and 4 and the second set 5, 6, 7 and 8. In FIG. 3 an alternativearrangement is used whereby each independent set of four paths has pathsselected alternately relative to the pipe axis. In FIGS. 3 a and 3 b,the first set of four paths would be A1, B1, C1 and D1 and the secondset A2, B2, C2 and D2. However, both of the arrangements shown sufferfrom a common weakness in that each group of four paths will still beaffected differently by distortions of the flow velocity field,particularly when complex non-axial flow fields such as asymmetricrotational are present. What will happen in such a case is that onegroup of four paths will produce a result that will overestimate theflow rate, whilst the other group will underestimate the flow rate.Whilst this has some use in diagnosing flow conditions, it complicatesthe process of meter verification, as it is difficult to distinguishbetween an error in the measurement system itself and a difference thatis created by the flow velocity field.

This limitation can be reduced in magnitude by use of a mechanical flowconditioning element installed upstream of the flow meter is employed toreduce the transverse flow components, but this negates the benefits ofa non-intrusive meter design.

A further disadvantage of the concept using two similar groups ofultrasonic paths such as shown in FIGS. 2 a, 2 b, 3 a and 3 b is thateven when a flow conditioner is used, some problems may be difficult todetect or quantify. If, for example, a uniform buildup of contaminationinside the meter body was to occur, then the output from each set offour paths would be affected equally, and detection of the problem wouldhave to rely on qualitative diagnostics such as amplifier gain, velocityprofile shape or comparison of sound velocities, as there would be noindicated difference in flow rates.

BRIEF SUMMARY OF THE INVENTION

The present invention is a self-checking ultrasonic flow meter thatprovides an output of flow rate plus an associated estimate ofuncertainty due to changes that could have affected the accuracy of themeasurement system. One aim of the invention is to ensure that theestimate of uncertainty is not affected by asymmetric rotational flows,therefore eliminating the need for mechanical flow conditioning. This isachieved by arranging transducers such that redundant measurements ofaxial velocity can be made in each chordal measurement plane of the flowmeter, i.e. multiple axial measurements are made in each chordal planein such a way that they are substantially independent of the effects ofnon-axial or transverse flow. This dictates that there should be aminimum of six nodes in each chordal measurement plane, where each nodeis either a single transducer or a single reflection point. The compoundaxial velocity measurements in each measurement plane are then used inthe computation of the flow rate, and comparison of individual in-planeaxial velocity measurements used in the assessment of the uncertainty.Another aim of the invention is to be able to detect path angle and pathlength changes that would result from contamination build up inside themeter body, and to be able to do this for each chordal plane withoutreference to the data from another chordal plane. To that end, thevelocity measurements within each chordal plane are made using pairs oftransducers arranged such that one path has a path length divided by acosine of the angle relative to the conduit axis that is different fromanother path in that same plane. Combining these constraints the flowmeter would have transducers forming a minimum of three traverses ineach chordal plane, at least one path having a path length or path anglethat is different to the others in that plane.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

In the accompanying drawings, the preferred embodiment of the inventionand preferred methods of practicing the invention are illustrated inwhich:

FIG. 1 shows a combination of a 4-path and a single-path meter in onebody of the prior art.

FIGS. 2 a and 2 b, and 3 a and 3 b show two different combinations of4-path meters in one body of the prior art.

FIG. 4 is an illustration of a single chordal measurement plane of thepresent invention.

FIGS. 5 a and 5 b are illustrations of the transit time measurementprinciple with axial and transverse velocity components shown.

FIG. 6 shows three direct paths in a single chordal plane.

FIGS. 7 a and 7 b show an arrangement of transducers and reflectors inone chordal plane according to one embodiment of the invention.

FIGS. 8 a and 8 b show an arrangement of transducers forming directpaths in one chordal plane according to one preferred embodiment of theinvention.

FIGS. 9 a and 9 b show an arrangement of transducers and reflectorsforming two direct paths and one reflected path in one chordal planeaccording to the invention.

FIGS. 10 a-10 f show various arrangements of transducers and reflectorswhere some are shared by two or more paths such that the total number ofnodes can be reduced to 5, 4 or 3. FIG. 10 a shows three direct paths ina single chordal plane with one transducer that is shared by all threepaths. FIG. 10 b shows two reflected paths with one transducer that isshared by both paths. FIG. 10 c shows two reflected paths with areflector that is shared by both paths. FIG. 10 d shows two direct pathsand one reflected path with one transducer that is shared by two pathsand with a combined transducer/reflector that is another shared node.FIG. 10 e shows two direct paths and one reflected path with threetransducers that are each shared by two paths. FIG. 10 f shows twodirect paths and one reflected path with two transducers that are eachshared by two paths and a combined transducer/reflector that is a nodethat is shared by all three paths.

FIG. 11 shows a meter with four chordal planes.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings wherein like reference numerals refer tosimilar or identical parts throughout the several views, and morespecifically to FIGS. 4, 5, 6, 7 a and 7 b thereof, there is shown anultrasonic flow meter 10 for measuring fluid flow in a conduit 26. Theflow meter 10 comprises multiple transducer pairs 12 positioned to formacoustic transmission paths 14 that are co-located in two or morechordal measurement planes 16, each plane having length to width ratioof less than 2.5. In each chordal measurement plane the transducer pairs12 located in the chordal measurement plane are positioned to formacoustic transmission paths 14 that traverse at least once from one side18 of the plane to another side 20 of the plane. If all paths 14 aredirect from one transducer 22 to another transducer 22 of a transducerpair, there is a minimum of three traverses in each chordal plane and ifany paths 14 employ a reflection point 28, there is a minimum of fourtraverses such that in either case a sum of the number of paths 14 andthe number of traverses in each chordal plane is greater than or equalto six. The flow meter 10 has a signal processor 30 to cause thetransducers 22 to produce the necessary signals and to receive thesignals produced by the transducers 22 and perform the necessary signalprocessing and computations. Such a signal processor 30 would be similarto those currently produced by Cameron International for the Caldon LEFMseries of flowmeters.

The ultrasonic flow meter 10 may have three paths 14 per chordal planeand transmission is on a direct path between individual transducers 22.The ultrasonic flow meter 10 may have two paths 14 per chordal plane,each path being a reflected path with two traverses of the chordal planeand one reflection in each of the two paths 14. The ultrasonic flowmeter 10 may have three paths 14 per chordal plane and transmission ontwo paths 14 is direct between transducers 22, and one path is areflected path with two traverses of the chordal plane and onereflection point.

The present invention pertains to an ultrasonic flow meter 10 formeasuring fluid flow in a conduit 26. The flow meter 10 comprisesmultiple transducer pairs 12 positioned to form paths 14 that areco-located in two or more chordal measurement planes 16 of the conduit26. In each chordal measurement plane transducers 22 of the transducerpairs 12 are positioned to form acoustic paths 14 that traverse at leastonce from one side 18 of the plane to another; at least one path has adifferent path length or angle relative to the other paths 14 in thatparticular chordal plane, such that a path length divided by a cosine ofthe angle relative to the conduit 26 axis is different from another pathin that same plane.

The present invention pertains to an ultrasonic flow meter 10 formeasuring fluid flow in a conduit 26. The flow meter 10 comprisesmultiple transducer pairs 12 positioned to form paths 14 that areco-located in two or more chordal measurement planes 16 of the conduit26, such that the paths 14 form a minimum of three traverses in eachchordal measurement plane.

The ultrasonic flow meter 10 may have three direct paths 14 per chordalplane whereby a first pair of paths 14 (A and B) are used in thecomputation of an axial velocity measurement in the plane, and a secondin-plane axial velocity measurement is made using one of the pathsbelonging to that first pair of paths and a third path such that thesecond pair of paths is defined as A plus C or B plus C.

The ultrasonic flow meter 10 may have three direct paths 14 per chordalplane whereby two in-plane axial velocity measurements are made in eachplane according to equations:

$v_{axialAB} = \frac{\left( {v_{B} - {v_{A}\frac{Z_{A}X_{B}}{X_{A}Z_{B}}}} \right)}{\left( {1 - \frac{Z_{A}X_{B}}{X_{A}Z_{B}}} \right)}$$v_{axialBC} = \frac{\left( {v_{C} - {v_{B}\frac{Z_{B}X_{C}}{X_{B}Z_{C}}}} \right)}{\left( {1 - \frac{Z_{B}X_{C}}{X_{B}Z_{C}}} \right)}$

Other presentations of these equations are possible; therefore it issolution of simultaneous equations to eliminate the transverse velocityin the solution that is important, not the specific form of the finalequation used.

The present invention pertains to an ultrasonic flow meter 10 formeasuring fluid flow in a conduit 20. The flow meter 10 comprisesmultiple transducer pairs 12 positioned to form acoustic transmissionpaths 14 that are co-located in two or more chordal measurement planes16. The length of a chordal plane 16 containing the paths 14 being lessthan 2.5 times the width of the plane 16. In each chordal measurementplane 16 the transducer pairs 12 located in the chordal measurementplane 16 are positioned to form acoustic transmission paths 14 thattraverse at least once from one side of the plane 16 to another side ofthe plane 15. Each transducer 22 or reflection point 28 defines a pathnode. The number of nodes per chordal plane 16 is equal to or greaterthan six.

In the case where any node is shared between one or more paths, thetotal number of nodes can be reduced accordingly. This would apply if acommon reflection point 28 it used for more than one path 14, or if amulti-directional transducer 22 is used at the end of two or more paths14. One example would be a chordal plane 16 where three direct paths 14are formed by using a shared transducer 22 at one side of the plane 16for one end of each of the three paths 14, and separate transducers 22at the other side of the plane 16 for the other end of each of the threepaths 14. In that case, the number of nodes would be reduced from 6 to 4as the second and third paths 14 are sharing a node with the first path14. Another example would be a chordal plane 16 where two reflectedpaths 14 are formed by using a shared transducer 22 for one end of eachof the two paths 14, separate reflectors 28 at the other side of theplane 16, and separate transducers 22 at the other end of each path 14.In that case the number of nodes would be reduced from 6 to 5 as thesecond path 14 is sharing a node with the first path 14. Yet anotherexample would be a chordal plane 16 where two reflected paths 14 areformed by using four separate transducers 22 for each end of the twopaths 14 on one side of the plane 16, and a shared reflector 28 at theother side of the plane 16. In that case the number of nodes would bealso reduced from 6 to 5 as the second path 14 is sharing a node withthe first path 14.

In a case where there are three paths 14 in a chordal plane 16 andtransmission on two paths 14 is direct between transducers 22 and onepath 14 is a reflected path 14 with two traverses of the chordal plane16, the number of nodes may be reduced from 7 to 5 if the two directpaths 14 share a transducer node between them at one end and another ofthe direct path transducers also serves as the reflector for thereflected path.

In another case where there are three paths 14 in a chordal plane 16 andtransmission on two paths 14 is direct between transducers 22 and onepath 14 is a reflected path 14, the number of nodes may be reduced from7 to 4 if the two direct paths 14 share a transducer node between themat one end and each share a transducer node at the other side of theplane with one or the other end of the reflected path 14.

In another case where there are three paths 14 in a chordal plane 16 andtransmission on two paths 14 is direct between transducers 22 and onepath 14 is a reflected path 14, the number of nodes may be reduced from7 to 3 if the two direct paths 14 each share a transducer node with thereflected path 14 and a third shared transducer node serves both pathsand also serves as the reflector 28 for the reflected path 14.

The present invention pertains to a method for measuring fluid flow in aconduit 26 with an ultrasonic flow meter 10. The method comprises thesteps of forming with multiple transducer pairs 12 positioned withrespect to the conduit 26 acoustic transmission paths 14 that areco-located in two or more chordal measurement planes 16, each chordalplane having a length to width ratio of less than 2.5 In each chordalmeasurement plane the transducer pairs 12 located in the chordalmeasurement plane are positioned to form acoustic transmission paths 14that traverse at least once from one side 18 of the plane to anotherside 20 of the plane. If all paths 14 are direct from one transducer 22to another transducer 22 of a transducer pair a minimum of threetraverses is desired in each chordal plane and if any paths 14 employ apoint of reflection 28 a minimum of four traverses is desired such thatin either case a sum of the number of paths 14 and the number oftraverses in each chordal plane is greater than or equal to six. Thereis the step of determining the fluid flow in the conduit 26 from signalsreceived by the transducers 22 after they have travelled along the paths14.

The present invention pertains to a self-checking flow meter 10 fordetermining fluid flow in a conduit 26. The flow meter 10 comprises aplurality of transducers 22 engaged with the conduit 26. The flow meter10 comprises a signal processor 30 in electrical communication with thetransducers 22 which causes the transducers 22 to transmit acousticsignals through the flowing fluid or receive flow signals from thetransducers 22 based on the transmitted acoustic signals the transducers22 receive and produces a measurement of flow rate and an associatedestimate of uncertainty due to changes that have affected the accuracyof the measured flow rate based on the acoustic signals.

The signal processor 30 may provide verification of axial velocity ineach chordal measurement plane of the flow meter 10 for accurateself-verification in the presence of complex non-axial flows includingasymmetric rotational flows, and in case of discrepancy providesidentification of which chordal measurement planes have contributed tothe discrepancy. The transducers 22 are arranged such that two or moremeasurements of axial velocity can be made in each chordal measurementplane of the flow meter 10 so the two or more in-plane axialmeasurements made in each chordal measurement plane are substantiallyindependent of the effects of non-axial or transverse flow. For this towork effectively, all paths must be closely spaced in order thatrotation and development of the flow in the axial direction does nothave a significant effect. In other words, if the paths are separated bytoo great a distance, the velocity profile and swirl pattern at separatepaths in the same chordal plane will be different and it cannot beassumed that the axial and transverse components of velocity are thesame at each path in the chordal plane. Therefore, the paths shouldpreferably overlap or the length of the chordal plane should be lessthan 2.5 times its width.

The signal processor 30 may detect path angle and path length changesthat would result from contamination build up inside the flow meter 10,and does this for each chordal measurement plane without reference todata from another chordal measurement plane. The transducers 22 may formmultiple transducer pairs 12 positioned to form acoustic transmissionpaths 14 that are co-located in two or more chordal measurement planes16, in each chordal measurement plane the transducer pairs 12 located inthe chordal measurement plane are positioned to form acoustictransmission paths 14 that traverse at least once from one side 18 ofthe plane to another side 20 of the plane, if all paths 14 are directfrom one transducer 22 to another transducer 22 of a transducer pair, aminimum of three traverses is desired in each chordal plane and if anypaths 14 employ a point of reflection 28, a minimum of four traverses isdesired such that in either case a sum of the number of paths 14 and thenumber of traverses in each chordal plane is greater than or equal tosix.

The measurement system of the invention comprises a section of conduit26 housing multiple ultrasonic transducers 22, each transducer 22 beingused in conjunction with at least one other transducer 22 in order tomeasurements of ultrasonic transit time along paths 14 inside theconduit. Transducers 22 are positioned such that all of the paths 14fall in a number of discrete chordal measurement planes 16. In thiscontext a chordal measurement plane is a plane that intersects twopoints on the boundary of the conduit, is parallel with the central axis24 of the conduit, and has a length to width ratio of less than 2.5 asshown in FIG. 4.

Either direct or reflected paths 14 can be used or a combination ofboth. In a direct path the ultrasonic signals travel between transducers22 without a change of direction via a reflection point. In a reflectedpath, the path is made up of two or more traverses of the interior ofthe conduit 26 by means of reflection. Reflected paths may requireinstallation of a reflector at the intersection with the conduit or mayuse the conduit 26 wall as a reflector. A direct path therefore includesonly one traverse across the chordal measurement plane, whereas areflected path includes multiple traverses. The current inventiondiffers from prior art in that the transit time measurements are used toobtain at least two values of axial velocity for each chordalmeasurement plane, derived in such a manner that each axial velocityvalue is substantially immune to any velocity component transverse tothe plane. This imposes certain conditions on the configuration of paths14 in each chordal measurement plane. In terms of the number of paths 14and traverses desired in each chordal plane, the minimum requirement isfor two paths of two traverses each if only reflected paths 14 are used.Three or more paths and three or more traverses are desired if anydirect paths are used.

With reference to FIGS. 5 a and 5 b, it can be shown with certainassumptions that the transit time associated with a single traverse ofan ultrasonic path can be represented as follows:

$t_{up} = \frac{L}{c - {v_{axial}\cos \; \theta} - {v_{transverse}\sin \; \theta}}$$t_{down} = \frac{L}{c + {v_{axial}\cos \; \theta} + {v_{transverse}\sin \; \theta}}$

Where L is the length of the traverse, c is the sound velocity,v_(axial) is the velocity component in the axial direction,v_(transverse) is the velocity component at 90 degrees to the axialdirection in the chordal measurement plane and θ is the effective pathangle. Introducing a calculated velocity term v for an individual pathwe can write:

$v = {\frac{L\left( {t_{up} - t_{down}} \right)}{2\; \cos \; \theta \; t_{up}t_{down}} = {{v_{axial} + {v_{trasverse}\tan \; \theta}} = {v_{axial} + {\frac{X}{Z}v_{transverse}}}}}$

Now, using an example of three direct paths as shown in FIG. 6, it canbe written,

$v_{A} = {v_{axial} + {\frac{X_{A}}{Z_{A}}v_{transverse}}}$$v_{B} = {v_{axial} + {\frac{X_{B}}{Z_{B}}v_{transverse}}}$$v_{C} = {v_{axial} + {\frac{X_{C}}{Z_{C}}v_{transverse}}}$

Where Xand Z are the projected path lengths on the cross-sectional andaxial planes and the subscripts refer to paths A, B and C respectively.

With a system of two simultaneous equations and two unknowns, it ispossible to solve for the two unknowns. In this case, there are threeequations and therefore we can obtain v_(axial) and v_(transverse) forthat particular chordal plane from multiple combinations of the data.For example, if v_(axialAB) is denoted to represent the axial velocitycalculated using the measurements from paths A and B, and v_(axialBC) torepresent the axial velocity calculated using the measurements of pathsB and C, then the above equations can be solved as follows:

$v_{axialAB} = \frac{\left( {v_{B} - {v_{A}\frac{Z_{A}X_{B}}{X_{A}Z_{B}}}} \right)}{\left( {1 - \frac{Z_{A}X_{B}}{X_{A}Z_{B}}} \right)}$$v_{axialBC} = \frac{\left( {v_{C} - {v_{B}\frac{Z_{B}X_{C}}{X_{B}Z_{C}}}} \right)}{\left( {1 - \frac{Z_{B}X_{C}}{X_{B}Z_{C}}} \right)}$

This gives us two measures of axial velocity in that particular chordalmeasurement plane (which we call ‘in-plane axial’ velocities), both ofwhich are independent of the transverse velocity in the plane. Thismeans that any difference between the calculated values of in-planeaxial velocity will highlight errors in either the transit timemeasurement terms or the geometric terms of the equation, and will notbe affected by transverse flow. Note that in this particular example, athird axial in-plane velocity v_(axialAC) can also be calculated.

Similar outcomes can also be obtained for more complex assumptionsincluding adaptations to include practical issues such as recessedtransducers and the inclusion of time delay corrections. Furthermore, asimilar treatment can be carried out for reflected paths, wherecancelation of transverse flow can be effected within individual paths.

Calculation of the axial velocity in each plane now proceeds as follows:

v _(plane) _(i) =ƒ₁(v _(axialAB) , v _(axialBC) , v _(axialAC), etc)

Where ƒ₁ represents a function used to combine the measurements, i.e. anaxial velocity for a chordal measurement plane i is derived from all ofthe in-plane axial velocity measurements obtained for in that particularplane, and hence uses all of the measurements from the paths 14 that liein that plane. One preferred method of combining the in-plane axialvelocities is performing a simple average. However, more complex methodscould be used, such as applying weighting factors to each of thein-plane axial velocities or selecting just one of the path combinationsto use, without departing from the spirit of the invention.

Flowrate is then calculated by combining together the axial velocitymeasurement from each of the measurement planes 16 (which we will nowcall the ‘plane velocities’), along with any desired geometric and/orcalibration factors, e.g.

Q=k _(h) k _(g) f ₂(v _(plane) ₁ , . . . , v _(plane) _(n) )

Where k_(h) represents a hydraulic correction factor, k_(g) represents ageometric factor, and f₂ represents the scheme used to combine the axialvelocity measurements in order to obtain a representative mean. Thiscould involve, for example, schemes such as Gaussian quadrature, wherethe measurement planes 16 are positioned parallel to one another atlocations predetermined by the number of planes 16 and the planevelocities are then weighted accordingly, e.g.

$Q = {k_{h}k_{g}{\sum\limits_{i = 1}^{n}\; {w_{i}v_{{plane}_{i}}}}}$

Alternatively, empirical or model based combination of the planevelocities could be used.

For determination of the uncertainty due to changes that could haveaffected the accuracy of the measurement system, the difference betweenin-plane axial velocities is calculated for each measurement plane.Using again the example of three direct paths 14 per plane it ispossible to calculate three difference values for the in-plane axialvelocities, e.g.

Δ_(AB−AC) =v _(axialAB) −v _(axialAC)

Δ_(AV−BC) =v _(axialAB) −v _(axialBC)

Δ_(AC−BC) =v _(axialAC) −v _(axialBC)

The uncertainty in the plane velocity would hence be functionallyrelated to the difference values:

u _(plane) _(i) =f ₃(Δ_(AB−AC) , Δ _(AB−BC), Δ_(AC−BC))

Alternatively, instead of using difference values, alternativecomputational method could be applied, for example, the ratios of thein-plane axial velocities or a standard deviation could be used as theinput to the uncertainty estimation.

The estimation of uncertainty can easily be illustrated by example. Inthis simple example the axial velocity in the measurement plane iscalculated using three direct paths 14, at angles of 75, 60 and 45degrees. Note that this represents only one plane of the meter 10, theresults of which would later be combined with the other planes 16 todetermine the flow rate and overall uncertainty. The followingparameters are used in the calculation for this example:

Axial velocity in the measurement plane: 10 m/s

Transverse velocity in the measurement plane: 1 m/s

Speed of sound in the fluid: 1500 m/s

Width of measurement plane: 0.1 m

Table 1 below illustrates the measurement results in the case of asystem operating with no errors. The in-plane axial velocities arecalculated from three separate combinations of paths A, B and C. Asthere are no errors present, and the transverse velocity is eliminatedin the calculation of the in-plane velocities, the three results forcombinations AB, BC and AC are the same, and hence when we compare themagainst the other, the calculated deltas are zero, as is the error inthe plane velocity.

TABLE 1 Individual paths A B C Angle (degrees) 75 60 45 X (m) 0.1000.100 0.100 Z (m) 0.027 0.058 0.100 Error in tup (ns) 0 0 0 tup (ns)69182.33 77282.26 94772.34 tdown (ns) 68855.27 76680.16 93794.54In-plane axial velocities Plane velocity AB AC CB Average Error (m/s)(m/s) (m/s) (m/s) (%) 10.00 10.00 10.00 10.00 0.00% Absolute deltas ABvs AC AB vs BC AC vs BC Maximum 0.00% 0.00% 0.00% 0.00%

Now an error of 2 nanoseconds can be introduced into the upstreamtransit time measurement (tup) on path A. As shown in Table 2, now whenthe in-plane axial velocities, AB, AC and BC are computed, threedifferent results are obtained. It is also found that there is now anerror in the plane velocity result. Examining the deltas when we compareour in-plane axial velocity measurements, we find that for thisparticular case the maximum deviation (AB vs BC) has a magnitude that istwice the error in the average axial velocity. Hence, there is ameasured deviation that can be directly related to the uncertainty bymeans of a sensitivity coefficient.

TABLE 2 Individual paths A B C Angle (degrees) 75 60 45 X (m) 0.1000.100 0.100 Z (m) 0.027 0.058 0.100 Error in tup (ns) 2 0 0 tup (ns)69184.33 77282.26 94772.34 tdown (ns) 68855.27 76680.16 93794.54In-plane axial velocities Plane velocity AB AC CB Average Error (m/s)(m/s) (m/s) (m/s) (%) 9.93 9.97 10.00 9.97 −0.34% Absolute deltas AB vsAC AB vs BC AC vs BC Maximum 0.42% 0.72% 0.31% 0.72%

In general, the delta values will exceed the error in the planevelocity, as a result of the plane velocity being calculated frommultiple in-plane axial velocities. However, under some circumstances,if more than one error is present, it is possible that they can combinein a way that alters the sensitivity coefficient. To provide additionalinformation and some protection against such circumstances, in-planetransverse velocities can also be calculated, compared and used in theuncertainty estimation. Following on from the earlier parts of thedescription, transverse velocities can be calculated as follows:

$v_{transverseAB} = \frac{\left( {v_{B} - v_{A}} \right)Z_{A}Z_{B}}{\left( {{Z_{A}X_{B}} - {Z_{B}X_{A}}} \right)}$

The technique developed here can be implemented in many different waysby someone skilled in the art. The following descriptions cover justsome of the possible implementations:

In the implementation shown in FIGS. 7 a and 7 b, a chordal planecontains two paths 14, each of which has a single reflection and twotraverses. Different angles have been selected for each path so as toallow detection of common-mode errors according to the invention. Inthis configuration, each path delivers an in-plane axial velocitymeasurement directly. Therefore, the comparison of the two paths 14 todetermine the uncertainty in that measurement plane serves the purposeof the invention in this case. As each reflected path cancels thecontribution to the measurement of non-axial component of flow, onerelative disadvantage of this particular configuration is that nomeasurements of non-axial flow are available to compliment the analysisof the axial velocities.

In the implementation shown in FIGS. 8 a and 8 b, the chordal planecontains three direct single-traverse paths, with no reflections. Again,different path angles have been selected for these paths so as to allowdetection of common-mode errors. With this configuration, any pair ofpaths 14 can be combined to yield both an axial and a non-axial flowvelocity, which in an advantage when compared with the embodiment ofFIGS. 7 a and 7 b and hence the arrangement in FIGS. 8 a and 8 b ispreferred.

FIGS. 9 a and 9 b show a combination of reflected and direct paths inone chordal plane. In this case there are two direct paths and onereflected path. The two direct paths can be combined to give one measureof the in-plane axial velocity and the reflected path will yieldanother. Yet again, the use of different path angles and path lengthswill facilitate detection of common-mode errors.

In each of the preceding examples, a minimum of two measures of in-planeaxial velocity are derived that are substantially independent of thetransverse flow velocity. In order for this to be achieved, a chordalplane should contain an arrangement of paths 14 where the sum of thenumber of traverses plus the number of paths 14 is equal to or greaterthan 6. For example, in FIGS. 7 a and 7 b, there are two paths each withtwo traverses so the so the sum of traverses plus paths equals six.Likewise in FIGS. 8 a and 8 b there are three paths each of which are asingle traverse, so the sum of traverses plus paths equals six. Morecomplex arrangements involving direct and reflected paths, or multiplereflections are also possible without departing from the spirit of theinvention. In FIGS. 9 a and 9 b, there are three paths, two of whichhave a single traverse and one of which has two traverses, so the sum oftraverses plus paths in that case is seven.

An alternative way of describing the same constraint is to consider eachtransducer 22 or reflection point 28 as a node in the chordal plane. Inthat case, FIGS. 7 and 8 show arrangements with six nodes each, and FIG.9 shows an arrangement of seven nodes, therefore the minimum number ofnodes per chordal plane is six. Arrangements with more than seven nodesare conceivable but add cost and complexity to little gain.

FIGS. 10 a-10 f show various arrangements of 22 and reflectors 28 wheresome are shared by two or more paths such that the total number of nodescan be reduced to 5, 4 or 3. FIG. 10 a shows three direct paths 14 in asingle chordal plane 16 with one transducer 22 that is shared by allthree paths 14, reducing the number of nodes required from 6 to 4. FIG.10 b shows two reflected paths 14 with one transducer 22 that is sharedby both paths 14, reducing the number of nodes required from 6 to 5.FIG. 10 c shows two reflected paths 14 with a reflector 28 that isshared by both paths 14, reducing the number of nodes required from 6 to5. FIG. 10 d shows two direct paths 14 and one reflected path 14 withone transducer 22 that is shared by two paths 14 and with a combinedtransducer/reflector 32 that is another shared node, reducing the numberof nodes required from 7 to 5. FIG. 10 e shows two direct paths 14 andone reflected path 14 with three transducers 22 that are each shared bytwo paths 14, reducing the number of nodes required from 7 to 3. FIG. 10f shows two direct paths 14 and one reflected path 14 with twotransducers 14 that are each shared by two paths 14 and a combinedtransducer/reflector 32 that is a node that is shared by all three paths14, reducing the number of nodes required from 7 to 3.

A second example follows in which the in-plane axial velocities arecompared in order to detect a uniform buildup of contamination on theface all transducers 22 in a single chordal plane. In this example weare considering a chordal plane situated at a distance of 0.809 timesthe radius of a circular conduit of 16 inches in diameter. Similar tothe earlier numerical example, this example uses direct paths only. Thepath angles selected were 45, 65 and −55 degrees and the path lengthswere chosen such that the transducers 22 would be slightly recessedrelative to the internal diameter of the conduit. A velocity of soundvalue of 1380 m/s was assumed for the liquid, and 2200 m/s was assumedfor the contaminant, representing a thin layer of hydrocarbon wax.

By simulation, the sensitivity factor relating the difference betweenthe calculated in-plane velocities and the measurement error wasdetermined in advance as a function of the measured transverse flow.Table 3 below shows the results when the axial flow velocity is 5 m/s,the transverse flow is zero and there are no measurement errors orcontamination build-up. In this table it can be seen that all threein-plane axial velocity measurements agree and hence the estimateduncertainty is zero.

TABLE 3 Path velocities Path A 5.000 m/s Path B 5.000 m/s Path C 5.000m/s In-plane axial velocties AB 5.000 m/s BC 5.000 m/s AC 5.000 m/sMeasured (average) axial velocity 5.000 m/s Acual error 0.00% Transverseflow   0% Difference max from min 0.000 m/s Sensitivity factor 2.1011Estimated uncertainty 0.00%

Table 4 shows the results when the axial flow velocity is 5 m/s, thetransverse flow is zero and there is a wax buildup of 0.02 inches oneach transducer 22 face. It can be observed that the velocitymeasurement in that chordal plane would be in error by 0.2% and that thedifference between the in-plane velocity measurements can be used topredict an increased uncertainty of 0.19%.

TABLE 4 Path velocities Path A 5.010 m/s Path B 5.011 m/s Path C 5.013m/s In-plane axial velocties AB 5.010 m/s BC 5.012 m/s AC 5.007 m/sMeasured (average) axial velocity 5.010 m/s Acual error 0.20% Transverseflow   0% Difference max from min 0.005 m/s Sensitivity factor 2.1006Estimated uncertainty 0.19%

Table 5 shows the results when the axial flow velocity is 5 m/s, thetransverse flow is 1 m/s and there are no measurement errors orcontamination build-up. It can be observed that taken individually theindicated velocities on individual paths (A, B and C) differ owing tothe transverse flow, and that looking at these three measurements itwould be difficult to determine whether or not an error is present, butthat when the in-plane velocities are calculated from path combinationsAB, BC and AC, the three results agree, and the analysis results in anestimate of zero additional uncertainty.

TABLE 5 Path velocities Path A 6.000 m/s Path B 3.572 m/s Path C 7.145m/s In-plane axial velocties AB 5.000 m/s BC 5.000 m/s AC 5.000 m/sMeasured (average) axial velocity 5.000 m/s Acual error 0.00% Transverseflow   20% Difference max from min 0.000 m/s Sensitivity factor 1.5891Estimated uncertainty 0.00%

Table 6 shows the results when the axial flow velocity is 5 m/s, thetransverse flow is I m/s and there is a wax buildup of 0.02 inches oneach transducer 22 face. It can be observed that, taken individually,the indicated velocities on individual paths (A, B and C) differ owingto the combined effects of transverse flow and the wax build up and thatlooking at these three measurements it would be difficult to determinewhether or not an error is present. However, when the in-planevelocities are calculated from path combinations AB, BC and AC andcompared, the three results do not agree exactly, and the uncertaintyanalysis results in an estimate of 0.19% additional uncertainty. It canalso be observed, that the sensitivity factor, is different in tables 4and 6, as this parameter is adjusted as a function of the measuredtransverse flow to maintain the correct relationship between themeasured difference between the in-plane velocities and thecorresponding measurement uncertainty.

TABLE 6 Path velocities Path A 6.012 m/s Path B 3.580 m/s Path C 7.162m/s In-plane axial velocties AB 5.010 m/s BC 5.012 m/s AC 5.006 m/sMeasured (average) axial velocity 5.009 m/s Acual error 0.19% Transverseflow   20% Difference max from min 0.006 m/s Sensitivity factor 1.5885Estimated uncertainty 0.19%

In practice, the invention will most likely be implemented inhigh-accuracy meter designs that would employ the invention in multiplechordal planes 16, such as the arrangement of four chordal planes 16,with three paths in each shown in FIG. 11. While this illustration showsthe same embodiment of the invention being used in each plane (i.e.three direct paths), it is also possible that different combinationscould be used, such as the arrangement of FIG. 7 being used in one planeand the arrangement of FIG. 8 being used in another.

Nomenclature

Chordal plane 16: A plane that intersects two points on the boundary ofa conduit and extends in a direction that is parallel with the centralaxis 24 of the conduit.

Path 14: Intended route of ultrasound transmission through the fluidbetween two transducers.

Chordal path: Any path that is confined to a single chordal plane.

Direct path: A path where the intended route of transmission is directlybetween two transducers and does not involve a change of direction bymeans of reflection.

Reflected path: A path where the intended route of transmission connectstwo transducers via one or more reflection points. The reflection pointcould either be the conduit wall itself, or a reflector designed toredirect the path partway along the route of transmission.

Traverse: A straight segment of a chordal path between any two points,either two transducers, two reflectors, or one transducer and onereflector. A direct path has only one traverse, a path with onerefection has two traverses, and a path with two reflections has threetraverses.

Node: A transducer site or reflection point that defines one end of atraverse.\

In-plane axial velocity: A measure of axial velocity that involves useof two or more traverses in a single chordal plane in order to obtain avelocity measurement that is substantially independent of any transverseflow component in that plane.

Axial velocity: The component of flow velocity in a direction parallelwith the central axis 24 of the conduit.

Transverse velocity: The component of flow velocity at 90 degrees to theaxial direction in the chordal measurement plane.

Although the invention has been described in detail in the foregoingembodiments for the purpose of illustration, it is to be understood thatsuch detail is solely for that purpose and that variations can be madetherein by those skilled in the art without departing from the spiritand scope of the invention except as it may be described by thefollowing claims.

1. An ultrasonic flow meter for measuring fluid flow in a conduitcomprising: multiple transducer pairs positioned to form acoustictransmission paths that are co-located in two or more chordalmeasurement planes, the length of the chordal plane containing the pathsbeing less than 2.5 times the width of the plane, in each chordalmeasurement plane the transducer pairs located in the chordalmeasurement plane are positioned to form acoustic transmission pathsthat traverse at least once from one side of the plane to another sideof the plane, if all paths are direct from one transducer to anothertransducer of a transducer pair there is a minimum of three traverses ineach chordal plane and if any paths employ a point of reflection thereis a minimum of four traverses such that in either case a sum of thenumber of paths and the number of traverses in each chordal plane isequal to or greater than six.
 2. The ultrasonic flow meter of claim 1with three direct paths per chordal plane whereby a first pair of paths(A and B) are used in the computation of an axial velocity measurementin the chordal plane, and a second axial velocity measurement in thechordal plane is made using one of the first pair of paths and a thirdpath such that the second pair is defined as A and C or B and C.
 3. Theultrasonic flow meter of claim 1 with three direct paths per chordalplane whereby two axial velocity measurements are made in each planeaccording to equations:$v_{axialAB} = \frac{\left( {v_{B} - {v_{A}\frac{Z_{A}X_{B}}{X_{A}Z_{B}}}} \right)}{\left( {1 - \frac{Z_{A}X_{B}}{X_{A}Z_{B}}} \right)}$$v_{axialBC} = \frac{\left( {v_{C} - {v_{B}\frac{Z_{B}X_{C}}{X_{B}Z_{C}}}} \right)}{\left( {1 - \frac{Z_{B}X_{C}}{X_{B}Z_{C}}} \right)}$4. The ultrasonic flow meter of claim 1, whereby a multi-directionaltransducer is used such that two or more paths have a beginning or endpoint that is a shared transducer.
 5. The ultrasonic flow meter of claim1, whereby a reflection point is common to two of more paths.
 6. Theultrasonic flow meter of claim 1, whereby a transducer also serves as areflection point reflection point for another path.
 7. An ultrasonicflow meter for measuring fluid flow in a conduit comprising: multipletransducer pairs positioned to form acoustic transmission paths that areco-located in two or more chordal measurement planes, the chordalplane's length containing the paths being less than 2.5 times theplane's width, in each chordal measurement plane the transducer pairslocated in the chordal measurement plane are positioned to form acoustictransmission paths that traverse at least once from one side of theplane to another side of the plane, each transducer or reflection pointdefines a path node, a number of nodes per chordal plane is equal to orgreater than six.
 8. The ultrasonic flow meter of claim 7 with threepaths per chordal plane and transmission is on a direct path betweenindividual transducers.
 9. The ultrasonic flow meter of claim 7 with twopaths per chordal plane, each path being a reflected path with twotraverses of the chordal plane and one reflection in each of the twopaths.
 10. The ultrasonic flow meter of claim 7 with three paths perchordal plane and transmission on two paths is direct betweentransducers, and one path is a reflected path with two traverses of thechordal plane and one reflection point.
 11. The ultrasonic meter ofclaim 7 wherein there are no shared nodes and there are only 6 or 7nodes.
 12. The ultrasonic meter of claim 7 wherein one node is shared bytwo paths and the total number of nodes can be reduced from six to five.13. The ultrasonic meter of claim 7 wherein one node is shared by threepaths and the total number of nodes can be reduced from six to four. 14.The ultrasonic meter of claim 7 wherein two nodes are each shared by twopaths and the total number of nodes can be reduced from six to four orfrom seven to five.
 15. The ultrasonic meter of claim 7 wherein threenodes are each shared by two paths and the total number of nodes can bereduced from seven to four.
 16. The ultrasonic meter of claim 7 whereintwo nodes are each shared by two paths and a third node is shared bythree paths and the total number of nodes can be reduced from seven tothree.
 17. The ultrasonic flowmeter of claim 7 where the paths in eachchordal plane overlap.
 18. An ultrasonic flow meter for measuring fluidflow in a conduit comprising multiple transducer pairs positioned toform paths that are co-located in two or more chordal measurement planesof the conduit; in each chordal measurement plane the transducer pairsare positioned to form acoustic paths that traverse at least once fromone side of the plane to the other; at least one path has a differentpath length or angle relative to the other paths in that particularchordal plane, such that a path length divided by a cosine of the anglerelative to the conduit axis is different from another path in that sameplane.
 19. A method for measuring fluid flow in a conduit with anultrasonic flow meter comprising the steps of: forming with multipletransducer pairs positioned with respect to the conduit acoustictransmission paths that are co-located in two or more chordalmeasurement planes, in each chordal measurement plane the transducerpairs located in the chordal measurement plane are positioned to formacoustic transmission paths that traverse at least once from one side ofthe plane to another side of the plane, if all paths are direct from onetransducer to another transducer of a transducer pair there is a minimumof three traverses in each chordal plane and if any paths employ a pointof reflection there is a minimum of four traverses such that in eithercase a sum of the number of paths and the number of traverses in eachchordal plane is greater than or equal to six; and determining the fluidflow in the conduit from signals received by the transducers from thepaths.
 20. A self-checking flow meter for determining fluid flow in aconduit comprising: a plurality of transducers engaged with the conduit;and a signal processor in electrical communication with the transducerswhich causes the transducers to transmit acoustic signals through theflowing fluid or receive flow signals from the transducers based on thetransmitted acoustic signals the transducers receive and produces ameasurement of flow rate and an associated estimate of uncertainty dueto changes that have affected the accuracy of the measured flow ratebased on the flow signals.
 21. The flow meter of claim 20 wherein thesignal processor provides independent verification of axial velocity ineach chordal measurement plane of the flow meter for accurateself-verification in the presence of complex non-axial flows includingasymmetric rotation of flows, and in case of discrepancy providesidentification of the chordal measurement plane or planes contributingto the discrepancy.
 22. The flow meter of claim 21 wherein thetransducers are arranged such that two or more measurements of axialvelocity can be made in each measurement plane of the flow meter suchthat each of the two or more axial measurements made in each chordalmeasurement plane are substantially independent of the effects ofnon-axial or transverse flow.
 23. The flow meter of claim 22 wherein thesignal processor detects path angle and path length changes that wouldresult from contamination build up inside the flow meter, and does thisfor each chordal measurement plane without reference to data fromanother chordal measurement plane.
 24. The flow meter of claim 23wherein the transducers form multiple transducer pairs positioned toform acoustic transmission paths that are co-located in two or morechordal measurement planes, in each chordal measurement plane thetransducer pairs located in the chordal measurement plane are positionedto form acoustic transmission paths that traverse at least once from oneside of the plane to another side of the plane, if all paths are directfrom one transducer to another transducer of a transducer pair, there isa minimum of three traverses in each chordal plane and if any pathsemploy a point of reflection, there is a minimum of four traverses suchthat in either case a sum of the number of paths and the number oftraverses in each chordal plane is greater than or equal to six.